In many natural populations, it can be observed that the net reproduction rate, Ro, which is constant in the Lotka age-dependent model of population dynamics, varies with changes in the total population and time as well as other factors. Since the value of the constant Ro must be approximate, there must also be some question of the validity of results from the Lotka model when Ro is near 1, where small changes in Ro can result in quantitative changes in solutions. To obtain a model in which Ro varies with population and time, we assume that the birth and death moduli, beta (a,P,t) & lambda (a,P,t), are functions of age, total population and time and assume a maximum life span L and gestation period tau greater than or equal to 0 and derive the system (1): D rho plus lambda rho equals 0 (D rho (a,t) equals lim(1/h) (rho(a plus h, t plus h)-rho(a,t))h yields 0) P(t) equals integral from 0 to L rho(a,t)da, rho(0,a) equals integral from 0 to L beta (a,P(t-tau), t-tau) rho(a,t-tau)da, where rho is the age distribution at time t. This model, which is a generalization of the Lotka and von Foerster-Gurtin-MacCamy population models, yields Ro as a function of P and t while providing a useful tool within the structure of the model for study of its solutions. It is this last property which appears to distinguish this model since little progress has been achieved to date in describing solutions of generalizations of the Lotka model. This system is shown to be equivalent to a pair of integral equations which reduce to a particularly tractable form for t greater than L plus tau and have been used by this author to establish bounds and asymptotic properties of solutions as well as the existence of periodic solutions of (1). These results show that this model behaves in a manner which is consistent with biological expectations and provide a useful framework for further investigation. An extensive theoretical study of the mathematical properties of (1) is proposed to facilitate its use in the applications.